Burton MacKenzie

Crosswalks: It's measurably more 'green' to wait for a break in traffic

noreply@blogger.com (burton mackenzie) — Mon, 15 Aug 2011 20:41:00 +0000

Many people try to be greener by walking instead of riding in a bus or car, and that's great. For pedestrians, crosswalks are a good demand-based way to stop traffic and get safely across the road. However, if you don't use crosswalks judiciously, you're not being as green as you think.

At a local crosswalk where I cross, typically from 10-30 cars will stop to let me across. The speed limit there is 50 km/h, or 14 m/s (although they're usually going a little faster). The vehicle traffic is varied, but in my region of the world there are a lot of pickup trucks. On the low end of mass, a Toyota Tercel car is 914kg, and on the high end a Ford F-350 truck is 4490kg. The approximate average mass of a local vehicle is 2702 kg.

A good measure of the energy "wasted" is the amount of energy required to return vehicles to their previous speed after they stopped for the pedestrian.

E = 0.5*m*v² = 0.5 * 2702 kg * (14 m/s)^2 = 260 kJ for the average vehicle, or between 2.6MJ and 7.9 MJ for 10-30 average vehicles.

These values might not mean much to the layperson, so I'll put it in terms of gasoline usage.

Gasoline has an energy density of approximately 35 MJ/litre. This means that, given 100% efficiency of transmutation from gasoline to kinetic energy, the average vehicle uses 7.4 ml of gasoline to go from zero to 50 km/h. En masse, 10-30 average vehicles will use a total of 74 ml to 220 ml of gasoline to get up to speed after I stop them.

But it's even worse than that. Most steel internal combustion gasoline vehicle engines have an average energy conversion efficiency of only 18-20% (and a limit of 37% efficiency). That is, on average, the cars and trucks are only using 20% of the energy contained in the gasoline; the rest of the energy is mostly spent on waste heat.

For my example crosswalk, it costs the environment 370 ml to 1.1 litres of burnt gasoline every time I stop traffic to cross the road!

Of course, a product of burning gasoline is CO2 released in the atmosphere, created at a rate of approximately 2.3 kg CO2 per litre of gasoline, resulting in 0.85 kg to 2.5 kg of CO2 dumped into the atmosphere so I can cross the street.

Problem Workaround: Pedestrians have a reasonable need to cross the street. The greenest way to do this at a crosswalk is to wait for a break in traffic so the least amount of cars have to stop.

Don't fall into the entitlement habit of forcing the cars to stop for you at the moment you want to cross; You are legally within your rights to do so, but it comes at a cost the the environment. If you can wait for a minute for a break in traffic, you might have the chance to save an entire litre of gasoline! Remember, Reduce is the biggest, most important aspect of "Reduce, Reuse, Recycle".

Burton MacKenZie www.burtonmackenzie.com

Best Compliment Ever

noreply@blogger.com (burton mackenzie) — Sun, 13 Feb 2011 04:13:00 +0000

I've had people write a lot of things about what I've written, but my current favourite is "You are the sort of lunatic that should be running the country". Thanks D.Quinn!

Aquatic Humans, Gorillas, and Crocs

noreply@blogger.com (burton mackenzie) — Mon, 03 Aug 2009 08:26:00 +0000

There are interesting arguments and evidence supporting the theory that an ancestor of homo sapiens had a semi-aquatic existence at one point, where they hung out in the water a lot, at least part of the time. If you haven't heard about this yet, here's the wikipedia entry, and here's a nice 17 minute TED video with Elaine Morgan.

One counter argument is that in Africa, where humanity evolved, semi-aquatic living would a have a risk of being attacked by aquatic animals such as crocodiles. I wondered what the distribution of gorillas and the distribution of crocodiles in Africa looked like. With a couple minutes of googling, I found two maps purporting to be the distribution of Gorillas in Africa (src), and the distribution of Crocodiles in Africa (src, the only one I could find). I coarsely scaled and overlapped them, and this is the result:

In this image, the crocodile distribution (grey) is widespread, and the Gorillas (red) appear to not share the same area as Crocs in the West, but they do in the East. There are two species of Eastern Gorilla, the Eastern Lowland Gorilla, and the Mountain Gorilla. The Mountain Gorilla lives nowhere near Crocs, and the Eastern Lowland Gorilla lives in lowland and mountain rainforests and subalpine forests.

The Western Gorillas do not generally seem to overlap with crocodiles and their habitat, and recently the Wildlife Conservation Society found more than 100,000 previously unreported gorillas have been living in the swamp forests of Lake Tele Community Reserve.

I don't know why I thought to look at gorillas first, as Chimpanzees are an even closer relative of humans, so I did the same thing with an image (src) of their distribution in Africa. The following is the same image as above, with the chimpanzee distribution in green:

As you can see, almost the entire distribution of Chimpanzees does not overlap with Crocodiles!

These images were taken from arbitrary sources on the internet, are coarsely scaled against each other, and I know nothing of their accuracies in distribution.

If these images are a coarse approximation of reality, it appears that the nearest neighbor species of Ape spends their time away from crocdiles. These maps in of themselves prove nothing, as these are maps of modern species and of questionable accuracy. However, if our human ancestors were living in similar regions as present day Apes, these maps suggest it is reasonable to suggest crocodiles weren't a problem for semi-aquatic ancestors of our genus, at least, not enough of one.

Burton MacKenZie www.burtonmackenzie.com

Do Customs Agents have the right to your DATA?

noreply@blogger.com (burton mackenzie) — Fri, 01 May 2009 18:23:00 +0000

I am not a lawyer. Seek local legal counsel first; you are responsible for your actions, not me.

As people become increasingly technological we proportionally keep more personal records and information on our portable data devices (e.g., laptops, iPhones, PDAs, etc). Previous to the data revolution, our deeply personal information (e.g., love letters from your wife, your financial dealings, etc) was safe at home, at a bank, or another physically disparate location. Customs did not have jurisdiction to look through information/data other than what you brought with you, and what their existing records on you were.

We are now in the position that some of your data is not necessarily on a portable device, but it is accessible by it. For instance, your google-drive might contain private information about you, and you can access it via your iTouch. A customs agent should have no more ability to search your remotely-accessible files any more than they could send somebody over to your place to retreive some personal files they would like to see. You may have your portable configured to link to your gdrive after a password is entered, but you should not provide the password to it for a search any more than you should provide a key for the customs agent to go search your home.

Be prepared - you may get turned back at the border - but they will be unable to take a copy of your filesystem because you are not carrying your filesystem; it is not on your person. Even if your portable were seized and confiscated (legally or illegally), they still would not get the remote data, and that is how it should be. In my country we have legal rights respecting protection from unreasonable search and seizure. Your remote files are not within the jurisdiction of a border patrol; they cannot search them.

Nobody likes a hassle, but if people do not stand up for their rights they will ultimately lose them, tiny step by tiny step. Stand up for your rights; refuse illegal searches. Keep your data remote.

If any lawyers for various nationalities want to comment and tell me what their laws/jurisprudence are, I'd be happy to hear from you.

Burton MacKenZie www.burtonmackenzie.com

Sums of Squares: Being Complex makes it Easy!

noreply@blogger.com (burton mackenzie) — Sat, 25 Apr 2009 02:42:00 +0000

Did you know that (42² + 111²)(2² + 5²) = (471² + 432²) = (639² + 12²)?

Neither did I until just a minute ago. It turns out that the product of two sums of two integer squares is also equal to two sets of sums of other integer squares, and it's easy to figure out what they are.

Leonardo Pisano Fibonacci showed this in Proposition 6 of "The Book of Squares" in the year 1225, and I have read that even Diophantus was aware of it some 1800 years ago, but it seems it was Leibnitz who first applied complex numbers to this problem. Complex numbers make this problem simple.

Take the general case,

(a² + b²)*(c² + d²)

which factors to the complex roots

= [(a + ib)(a - ib)]*[(c + id)(c - id)]

rearrange the factors to get

= [(a + ib)(c + id)]*[(a - ib)(c - id)]

which multiplies out to

= [ (ac - bd) + i(ad + bc) ] * [ (ac - bd) - i(ad + bc) ]

but since this is a complex conjugate, it simplifies to

= (ac - bd)² + (ad + bc)²

That is, given any product of sum of squares, you can easily find what other sum of squares represents the answer.

Further, we can also re-order the factors to give

= [(a + ib)(c - id)]*[(a - ib)(c + id)]

= [ (ac + bd) + i(bc - ad) ] * [ (ac + bd) - i(bc - ad) ]

= (ac + bd)² + (bc - ad)²

Which is yet another solution represented as a sum of squares!
Try it! (42² + 111²)(2² + 5²) = (471² + 432²) = (639² + 12²)

Burton MacKenZie www.burtonmackenzie.com

Happy Pi Day!

noreply@blogger.com (burton mackenzie) — Sat, 14 Mar 2009 06:59:00 +0000

In honour of Pi Day, I ate a whole Pi!

Burton MacKenZie www.burtonmackenzie.com

Pi Day Update: I am disturbed by this video. I love it!

The Sun as seen from other Planets

noreply@blogger.com (burton mackenzie) — Mon, 23 Feb 2009 05:27:00 +0000

If you were standing on another planet in our Solar System, the size of the Sun's disk in the sky would be different than the size it looks from Earth. Below is an image I made of how large the Sun looks from every planet. Earth is shown in a brighter yellow to help your sense of scale.

From the perspective of lonely Neptune, our Sun just looks like a bright star. Pluto is not included in the diagram, but its visage of the Sun is the same as Neptune's: a bright star in the distance.

I'm already freaked out by how big the Sun is as seen from Earth - imagine being on Mercury, confronted by that giant ball of nuclear radiation! Its visible disk is almost 7 times bigger than it is on Earth!

Burton MacKenZie www.burtonmackenzie.com

p.s. Here is an earlier post about Mercury.

Why do so many people wonder if Ann Coulter is a man?

noreply@blogger.com (burton mackenzie) — Sun, 01 Feb 2009 19:11:00 +0000

Last year I was playing with the automated Gender Guesser. There were stirrings on the net that Ann Coulter, an american who makes a living by spewing controversial nonsense and hatred to the ignorant masses, was really a man. I went to her website and input some of her posts into the Gender Guesser.

The Gender Guesser is not a predictor. It cannot predict definitively whether or not somebody is a man or a woman any more than being a smoker predicts you will get lung cancer. At best, it might give results like "In a room of 100 people, if they all wrote this way, 70 (-ish) of them would be men". That is, there is a lot of room for error, nor can it predict an individual.

Nonetheless, as a lark I published its claim (with appropriate disclaimers of accuracy) that her own writings betrayed her as a man because of what the Gender Guesser reported.

Sadly, outside of short spikes of popularity, this has become my most popular post on my entire blog, a popularity almost exclusively based on daily google searches for "Ann Coulter is a Man" or "Is Ann Coulter a Man?". I am not proud of this - my blog is mostly math and science based. It is a thorn in my side that my most popular post is due to people searching for information on her true gender and that, on average, it far outcompetes my regular posts. I considered removing the original post entirely, but that didn't seem right, either. I was reluctant to even add this post, but in the end decided to publish the bizarre website traffic happenings that I've been seeing for months. This has been going on for a while but I didn't want to lead in January by mentioning it. Mentioning Ann is a bad Juju way to start a year.

Ann, I don't care if you're really a man or not. If you want to say you're a woman that's fine with me. Saying you were a man on the Lou Dobbs show didn't help, even if you were joking. I really do wonder, though, why so many people every freakin day come to my blog from google searches wondering if you're a man. WTF? No, seriously.

Burton MacKenZie www.burtonmackenzie.com

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Peasant Finger Multiplication Proof for all Bilaterally Symmetric Species

noreply@blogger.com (burton mackenzie) — Fri, 30 Jan 2009 08:24:00 +0000

There is a technique for multiplying numbers between 6 and 10 on your fingers called peasant multiplication (graphic illustration). I explained how to do it two years ago, and I mentioned an easy proof of it. Since I was subsequently asked for the proof, I present it now with an improvement. (If you don't already know how to perform the multiplication, please check the links above, first)

Why Peasant Finger Multiplication works for any Bilaterally Symmetric Species

As long as your fingers (or tentacles) on each hand (or appendage) are bilaterally symmetric and you count in a base defined by your total number of fingers, this method will work. First, let's start with definitions:

Since "digits" has different meanings in physiology and math, I will say "digits" when I mean mathematical place-value digits, and "fingers" when I mean dangly meat appendages with which you are counting/multiplying.

let n = factor #1 to be multiplied

m = factor #2 to be multiplied

p = product n * m

d = the number of fingers on each hand (total fingers on both hands = 2*d)

Since we (humans) count each number (n or m) from 6 to 10 on a hand with 5 fingers, the actual number of fingers used on a hand would be n-5, or more generically for any species,

a = n - d (number of fingers used on one hand)

b = m - d (number of fingers used on other hand)

If the product p for which we are searching is defined as

p = n * m

then

p = n * m = (a + d)*(b + d) = ab + d*(a+b) + d²

With peasant math, the tens digit (base 10) is represented by adding the number of fingers on each hand representing digits. Here I multiply it by 10 to represent that it will be placed in the 10s digit:

p₁₀ = 10*(a + b)

or more generally for any species, the "d's" digit is,

p_d = 2*d*(a + b)

Similarly, for the value of the ones digit, you add the remaining (unused) fingers on each hand:

p_ones = (d - a)*(d - b)

which expands to

p_ones = d² - d*(a + b) + ab

In peasant math, the product p is acheived by combining the 10s digit with the ones digit:

p = p_d + p_ones = 2*d*(a + b) + d² - d*(a + b) + ab

= ab + d*(a+b) + d^{2 =} (a + d)*(b + d)

= n * m

which is the original definition of the product you are seeking to find.

Peasant math works, regardless of your species, as long as you're bilaterally symmetric and your numeric base is that of your total number of fingers, tentacles, or tough scaly claws.

Burton MacKenZie www.burtonmackenzie.com

Multiplying big numbers using Cosines

noreply@blogger.com (burton mackenzie) — Sat, 24 Jan 2009 19:07:00 +0000

I came across a technique for multiplying big numbers recently, called prosthaphaeresis [1], that predates the use of logarithms. It relied on the use of pre-calculated cosine tables, and made use of the trigonometric relation:

cos(A)*cos(B) = [ cos(A+B) + cos(A-B) ]/2

All you need to to is scale the two large numbers to between 0 and 1, look up the scaled numbers in your cosine table to find the angles they represent, add and subtract the angles, find the cosines of the new angles in your table, and average them.

This speeds up multiplication by reducing a series of single-digit multiplications and additions to some table lookups, three addition/subtractions, and a division by two. Before calculators, computation was much more of a scarce resource; anything that could speed it up was useful. Before logarithms were invented, this could speed up your multiplication a lot.

For example, let's say we wanted to multiply 45678 x 23456. Convert them to (0.45678 x 10^5) x (0.23456 x 10^5). Combine the two multiplied 10^5 base 10 exponents into 10^10 and save it for later. Looking up 0.45678 and 0.23456 in the cosine table says the angles representing them are 62.820 and 76.434 degrees, respectively. Adding and subtracting these angles gives new angles of 139.254 and -13.614. The cosines of these angles are -0.75761 and 0.97190. Averaging them gives 0.10715. Multiply this by the base 10 exponent of 10^10, and you have 1071400000.

By my calculator, 45678 x 23456 = 1071423168, which to the correct number of significant figures, is 1071400000, the same answer from the cosine method. Pretty neat, for the days before calculators.

Burton MacKenZie www.burtonmackenzie.com

[1] Greek "prosth-" or "adding" and "-aphaeresis" or "subtracting"

A Green Energy Business Model

noreply@blogger.com (burton mackenzie) — Thu, 25 Dec 2008 06:01:00 +0000

I just recently heard about a new sustainable-power business model. It would work best in areas where cost of electric power rates are in the medium to high range. I hope it takes off.

Customer: Warehouses, BigBox businesses, etc. It could be any operation that consumes power (for lighting, machinery, etc) and has an open roof sprawl.

Technology: Solar panels on the roof collect cheap energy to reduce higher energy costs paid to local grid power company. Solar power on the roof could supply approximately 20% of the electrical needs of the business.

Problem: Solar power installed on the roof would be expensive up front. The power costs are only cheaper when amortized over decades. It requires skilled maintenance, which is not the core competency of the business.

Solution: A third party business whose core competence is solar power purchases the equipment and maintains it. The Big Box business signs a 20 year contract to buy all the solar power supplied from the roof by the 3rd party business.

Everybody's Happy: The Big Box business saves on energy costs. The 3rd party power company makes money and employs people. The citizens get cleaner power generation used in their environment. Ubiquitous solar power will drive down cost, making it even more competitive.

I think this is the first time I've ever gotten excited about a business model. Merry Christmas.

Burton MacKenZie www.burtonmackenzie.com

Net Neutrality: Internet ~ Electricity

noreply@blogger.com (burton mackenzie) — Fri, 19 Dec 2008 06:30:00 +0000

My internet has been down for almost a week.

It's been like turning off the electricity. Sure, you can live without it, but it really makes a lot of things easier.

How long is it before our functional society is so deeply embedded into a bidirectional commodity data service (i.e. the internet) that it will collapse without it? At one technological company where I worked, during an internet outage the apathetic network guy told the president he'd "get around to fixing it later". The president pretty much flipped out on him, as lack of internet brought the productivity of the engineering design team to zero. The network guy, of all people, did not understand this.

If a commodity data service can be comparable to commodity energy (e.g. electricity, natural gas, etc), why would you pay more for the end use of the service? You do not pay a different base rate for electricity if you're using it for your stove instead of your laptop. That would be crazy. Similarly, you should not be charged differently depending on if your data is used for email, surfing, or downloading mp3s. Data should be charged at a rate of amount of data actually transferred (i.e. how much of the commodity did you use), with other commercial factors like average bandwidth, latency, etc.

If the power company wanted to charge us different rates depending on the nature of what you were using it for, there would be revolt in the streets! That is an artificial business model based solely upon squeezing more money out of the consumer, not based on costs of supplying the commodity.

That is what Net Neutrality is about. Data is a commodity service, like electricity. By allowing coporations to charge you based on the intended use of the data rather than proportional to the actual costs of supplying the service, they are imposing an artificial business model, for the good of them, not you. Regardless of what their propaganda tells you, it is only about more money for the corporations supplying the data service. There should be revolt in the streets if this ever happens. Do not let it. Data must be neutral!

Control the nature of the data service, and control the blossoming massively parallel interconnected society. I do not believe corporations should have a grip on our balls. Do you?

Burton MacKenZie www.burtonmackenzie.com

Why it's good to DISagree

noreply@blogger.com (burton mackenzie) — Fri, 21 Nov 2008 07:11:00 +0000

I heard some wisdom last week that got me thinking: It's more important to listen to people who disagree with you rather than those who do agree.

Those who agree with you will never encourage you to examine the beliefs for correctness/validity; there is little corrective feedback for mistaken ideas. Those who disagree with you will help you illuminate the validity/correctness of things you believe to be true, and help you discard the ideas you hold that fall apart under a different light. Those who disagree with us propel us towards knowledge, or we propel them, incrementally driving each other towards knowledge.

But there's no need to be a dick about it.

Burton MacKenZie www.burtonmackenzie.com

Amazing Properties of Numbers in base Golden Ratio

noreply@blogger.com (burton mackenzie) — Fri, 14 Nov 2008 09:14:00 +0000

What if 7 was the same quantity as 34? And 142.001529 as well? That seems like an impractical crazy number system, but those can be the most fun, so I'm going to show you one.

The number system we most commonly use is a base 10 place-value system. A number is described by digits from 0 to 9, and the position of each digit denotes the exponent of the base, multiplied by the value of the digit. For instance, 341 = 3*10² + 4*10¹ + 1*10⁰. In binary (base 2), each digit represents a power of two, e.g. 2⁵2⁴2³2²2¹2⁰. 2^-1 etc. With these bases, each quantity has only a single representation. For instance in base 10, 2 is equal only to 2 [1] and no other finite number [2].

This is what we consider normal and natural. However, if we choose an irrational number such as the golden ratio as the base of a number system, we get something entirely different.

In an earlier post I derived the golden ratio, showing its origin from the equation φ = 1 + 1/φ. Rewrite it as φ² = φ + 1. Since the digits in base φ represent exponent multiples of φ, all numbers take the form of φ² φ¹ φ⁰, etc. In base φ, the equation above can be directly represented as numbers, stating

1* φ²+ 0*φ¹ + 0* φ⁰⁼0*φ² + 1*φ¹ +1*φ⁰

or simply, 100_φ = 11_φ, or even more simply 100 = 11 (assuming base φ). This demonstrates that a number in base φ has non-unique finite representations! One number (100) can be represented as another (11). Multiplying or dividing the original equation by φ shows that we can apply this rule universally. Just as 100 = 11, 1000 = 110, 10 = 1.1, 0.001 = 0.00011, etc.

The next question is how many representations does each number have in base φ? Look at the case of 100 again. 100 can be represented as 11, 11 can be represented as 10.11, 10.11 can be represented as 10.1011, 10.1011 can be represented as 10.101011, ad infinitum. Not only are finite numbers in base φ representable in non-unique ways, there are an infinite number of ways to finitely represent any number in base φ!

Now that's a fun number system!

Burton MacKenZie www.burtonmackenzie.com

[1] Even for large values of 2!

[2] strictly speaking, 2 can also be represented in base 10 as an infinite series, 1.9999999....

Biomass Gassification: Off -grid energy generation

noreply@blogger.com (burton mackenzie) — Fri, 07 Nov 2008 09:14:00 +0000

Alternative energy generation is a multi-faceted problem. I strongly believe that we should have as many energy-generation technologies as we possibly can in operation at any given time. A wide-ranging diversity of energy sources is as important as genetic diversity of crops; if some fall to a blight or the cold, other varieties will fare all right. Andean potato farmers do this. It ensures survival by maintaining a stable food supply. Energy generation now means survival for a significant chunk of the world, especially those in hostile environments. We need it to be diverse to maintain a stable energy supply.

Ben Peterson from VictoryGasworks.com made the following video of him building a gassifier, which supplies a portable 6kW generator that runs an arc welder. The gassifier runs on yard waste such as woodchips or compressed pellets. I am impressed.

Burton MacKenZie www.burtonmackenzie.com

Our place in the cosmos - the survival of our species [video]

noreply@blogger.com (burton mackenzie) — Fri, 31 Oct 2008 08:14:00 +0000

In this video, Physicist David Deutsch delivers his monologue: "What is our place in the cosmos?". Parental Guidance: This video contains sobering thoughts.

Burton MacKenZie www.burtonmackenzie.com

The Road Less Traveled By

noreply@blogger.com (burton mackenzie) — Fri, 24 Oct 2008 16:33:00 +0000

I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I—
I took the one less traveled by,
And that has made all the difference.

--Robert Frost, "The Road not Taken"

Great Sci-Fi TV Intros

noreply@blogger.com (burton mackenzie) — Fri, 26 Sep 2008 05:12:00 +0000

When I think back to Science Fiction television shows with great musical introductions, these are the ones that immediately play in my brain. Apparently I'm big on guitar riffs.

Space 1999

I loved watching Space 1999. It rarely failed to entertain me or keep me on the edge of my seat. One commenter on IMDB described the storylines as "No 'Space as the last frontier' rhetoric, here. Space is cold and mistakes are lethal. That increases the realism even if 1999 is well past. Action progresses like a slowly unfolding bad dream." That's a great simile, and accurate.

Red Dwarf

Red Dwarf is a British SciFi comedy. It's a slightly darker comedy, but the novels are even darker. Both are hilarious.

Dr. Who

This theme is forever burnt into my brain. It has a uniquely distinctive sound. There's an interesting history on how the original theme was made, the first fully electronically made theme at the time. The synthesizer-like tones sound so pure it reminds me of a theramin mixed with a glass harmonica. It isn't quite as upbeat as the first two, but I love to hear it.

Do you have a favourite scifi TV theme? Link to it in the comments!

Burton MacKenZie www.burtonmackenzie.com

Garbage Can Art

noreply@blogger.com (burton mackenzie) — Fri, 19 Sep 2008 05:12:00 +0000

As much as I love guerrilla installation art, I have long despised most graffiti. Perhaps it's a fine line to draw, but install art I appreciate is more trivially removable. Most of the graffiti around here is merely lame name tagging; it is rare to find art. When art is created, the taggers are soon on hand to wipe their shit on it.

Today I found some graffiti that is more on the artistic side. It's no Banksy, but it's better than tags. Seriously, this is the best the painted graffiti gets around here.

Counting the feathers (?) counter-clockwise, the star is above feather #26. There is a local group that does install art (and sometimes graffiti) called the 26ers, but this is most likely a coincidence. Notice the brighter white paint that enters the painting from the left. It's from some lame tagger who can't bear to not have their name pissed on something. Not cool, tagger. Not cool.

Burton MacKenZie www.burtonmackenzie.com

p.s. This one was found a stone's throw away from the site of another small piece, long since removed.

Visa Gold as a source of the Golden Ratio?

noreply@blogger.com (burton mackenzie) — Fri, 12 Sep 2008 05:12:00 +0000

The Golden Ratio is a number that appears all over in nature and design. It is occasionally an optimal point in natural growth (amongst other things), and nature always tends toward the optimal.

I've been doing some research into its incarnations lately. A website I found had some good info, but it also had a lot of crap pseudo-science, so everything on the website was suspect. One claim it made was that dimensions of credit cards were really close to the golden ratio. To be fair, the website doesn't try and draw some cosmic significance from this, but given what I've read on the rest of the site I feel that some kind of significance is implied. (although I'm not sure what)

I figured it is possible that there is some sort of manufacturing material ratios that are optimal for using the golden ratio, but I didn't know for sure. What's good about this type of urban legend is that it is easily measurable, thus easy to verify or disprove. And if you know me, you know that when I don't know something, it really sticks in my craw. Of course, I had to examine the problem.

The standard dimensions of a credit card are 85.60 × 53.98 mm (a x b, as in the image above), as defined in the specification ISO/IEC 7810. The ratio of these dimensions (a/b) is 1.586, which is 2.0% lower than the golden ratio at 1.618, but that's not necessarily a problem.

I think credit cards are manufactured by punching them out of plastic rolls or sheets [1], but I've only seen them in post-punched stacks. Before punching, they would have a fixed border around them which becomes a waste/recycled product after the cards are punched out. If there were some manufacturing advantage to using the golden ratio, it would be the card+border dimensions of uncut material that should be the golden ratio, not those of the punched out card.

If the dimensions of the card are a x b, and each dimension has a fixed pre-punch border of w/2, then the pre-punched card area would be (a + w) x (b + w). In the ideal case where the ratio of the two dimensions is the golden ratio,

φ = (a + w) / (b + w)

Rearranging to find what the added border must be to get the golden ratio, given the size of the cutout,

w = (b*φ - a) / (1 - φ )

As well as using the official dimensions, I used a micrometer to measure the dimensions of a Visa, Mastercard, Bank Debit Card, and my work ID card which has a similar looking size. The following table captures the added border, w (as per the equation, above), so the uncut dimensions of each card reflect the golden ratio. The borders based on actual measurements has an accuracy of +- 0.02mm. As expected, every card was slightly smaller than the spec.

(Note: This giant extra space wasn't here in the preview. I'll try and fix this soon)

Card measured	Needed border, w
Specification	-2.82mm
Visa	-2.69mm
Mastercard	-2.57mm
Bank	-2.71mm
Work	-2.69mm

What these negative values means is that in order for the dimensions of a credit card to be the golden ratio, each dimension would have to shrink by 2.8 millimetres (approximately). This is a reduction of 3% or 5% for each dimension, depending on which one it is. It is clear that credit cards are not manufactured to accurately represent the golden ratio.

However, even though the dimensions do not accurately represent the golden ratio, it's still believable that it was a conscious consideration in the design. The golden ratio is often a numerically optimal point in design, but frequently, operating near the optimal point is just as reasonable, given other design tradeoffs. In this case the tradeoffs may be the dimensions of the raw materials or other manufacturing issues.

There are other reasonable explanations why credit card dimensions are close to the golden ratio. There may be a legacy size issue, such that when credit cards were conceived they had to fit inside slots in wallets originally made to hold business cards (although business cards have a different standard size). Further, the size could be most simply explained in that we humans tend to perceive dimensions that are based on the golden ratio as esthetically pleasing. Simply put, a card size may have been chosen that looked pleasing, and we found it pleasing because it was close to the golden ratio.

Also, if you're a secret math nerd you can measure your own credit cards and use the equation I gave for w to determine how much you must trim from each side to make the ratio of your credit card dimensions a golden one. [2] With the limits of scissors, you could probably even just use the number that was generated by the spec, trimming as close as you can cut to 2.82 mm. [3]

I declare that the urban legend of credit card dimensions being related to the golden ratio as "plausible", whether it is intentional or not. Mine are now intentional.

Burton MacKenZie www.burtonmackenzie.com

[1] If you know better, please let me know. I could find no references to their physical manufacture online.

[2] Don't forget to divide by 2 if you're trimming opposing sides, as in that equation each side has a border of w/2, giving a total of w for that dimension (a or b).

[3] If instead you choose to trim each of the four sides, use half this value, or 1.41 mm. For those who don't immediately recognize this number, it is the square root of two. Don't freak out. It's only true to three digits, and the specification gives us four, so it's just a one-in-a-thousand coincidence. Unless the finitely valued almost-√2 is really some other irrationally reminiscent, but finitely represented, distance away from something else notable. Maybe I've just started a new urban legend. ;-)

Star Trek promotes bestiality

noreply@blogger.com (burton mackenzie) — Fri, 05 Sep 2008 05:21:00 +0000

In the Star Trek universe, we keep meeting half-human half-alien beings but we never think about what it would have taken to produce them. There are a plethora of mixed-species characters, such as Mr. Spock, one of those most beloved of the original characters (a Vulcan/Human mix), Deanna Troi (Betazoid/Human) and B'Elanna Torres (Klingon/Human).

Intelligent life in the Star Trek universe evolved separately on their home planets from primordial ooze. [1] Even if all the aliens evolved from the same ooze as us [2], the genetic differences between us and any other space-faring species would be so large that we'd have a better chance of conceiving a child with an oak tree (they're genetically closer). [3] The Chicken Lady is more probable than Mr. Spock.

Ok, this is all science fiction. We don't have faster than light travel either, and it doesn't detract from the story. What does it matter? Fiction is fiction. Made up. Not real.

Warning: NSFW image to follow

What I find interesting about this isn't the content of Star Trek itself, but the public acceptance of the underlying assumptions to this; something the public at large would normally not accept in a different context. In this case the underlying assumption that generations of people have accepted without further thought is that inter-species sexual play is acceptable. If it's OK for people to have sex with a hot bodied vulcan (see image below), a totally unrelated species, where do we draw the line? Is it OK for people to have sex with more closely related species like oak trees, elephants, or octopuses? Where is the line of bestiality?

Figure 1: Sweet sweet non-human massage

We generally don't accept that it's OK for people to have sex with any old living thing they want. The difference between all these aliens and any living thing is that the aliens ostensibly have intelligence and can consent to the activities [4]. If that is our metric, then hamster sex is definitely out. That doesn't solve all the problems, though. There are plenty of similar enough intelligent and consenting cases right here on Earth.

Dogs are somewhat intelligent, and have been known to be sexual partners of humans [5]. To clear debate about consent, it is easy to find videos where male dogs willingly and eagerly insert themselves into human females. Have you ever had a dog hump your leg? It's worse than that. This specific canine-sapient sex a good example where the animal has given "consent" by acting of their own volition, and human-level intelligence is not required for it. Most of us think this is wrong.

Dolphins are believed to be reasonably intelligent, and in fact have bigger brains than humans and arguably similar cognition. Unfortunately, I've also found a website where a man describes his allegedly consensual dolphin sex. If this hasn't already crossed the intelligent/consent line for when nonhuman-human sex is OK, then we're perilously close to it. I'm still disgusted.

If we're prepared to accept Star Trek alien sex, we should also be prepared to accept tentacle sex. I'm of the belief that aberrant sexual relations between consenting adults is just fine. As long as you're an adult and everybody consents, knock yourself out. I can't say that I like the idea of my neighbor having a sexual relationship with something that lives in his pond and has thirteen eyes, but if I don't want to be a hypocrite I must support xenophilia. Otherwise, how would I get to do that hot vulcan?

Burton MacKenZie www.burtonmackenzie.com

[1] Well, almost. There are other immortal omniscient beings like Q. Who knows where they're supposed to come from.

[2] As we all did in the Star Trek: The Next Generation episode "The Chase".

[3] Internet rule 34 says that some people are already arborphilics. I suppose the webpage about it says it, too.

[4] We're not talking about a legal definition of consent, here. Animals have no ability to give consent under the law. I am talking about a definition where a bunch of people would say "yeah, the animal clearly wanted to do that".

[5] I'm not going to give you any links to this - google it yourself, but caveat emptor. Things can't be unseen. I'm doing you a favour by not providing a link.

Golden Ratio video

noreply@blogger.com (burton mackenzie) — Fri, 29 Aug 2008 05:21:00 +0000

This is a short and pretty video about the Golden Ratio [1]. I love the high level treatment (i.e. no hard math) and photographs of nature, which brings the beauty of the Golden Ratio to a wider audience.

The Golden Ratio is an optimally efficient point of operation for elements of growth in nature. That is the reason we find it so much! Like a ball rolling down a hill, coming to rest in a valley, nature always tries to optimize for the minimal energy configuration. Here we often find the Golden Ratio.

In the video they showed a resistive ladder, which also caught my eye because I recently discovered a similar circuit configuration whose solution contains the Golden Ratio as well. (Coming in a future post sometime)

Burton MacKenZie www.burtonmackenzie.com

[1] This video was made by a team of 4, including cmegans, who uploaded this video to youtube. Nice work. Click directly on the video (but not in the centre), and I believe it will open a window directly with youtubes page. Or click on the centre to watch it here.

Robotman, The Admiral, and Crazy Ed

noreply@blogger.com (burton mackenzie) — Sun, 24 Aug 2008 07:32:00 +0000

I recently read about a librarian who was fired for writing a book with characters based on odd library patrons. I don't know enough to comment on her case, but without further information, I don't see how this merits outrage.

When I was young and working in retail we had lots of different nicknames for different characters that would frequent the store, but they weren't meant to be derogatory. They were functional names for otherwise nameless cash customers.

RobotMan
For instance, there was "Robotman". He was a polite quiet man in his late 20s or early 30s. Every week he'd be in to buy some resistors or relays or some such thing. Every time he'd hang out in the components section, studiously reading the backs of the packages, reading about the parts inside. He would study the parts for 20 minutes to an hour, never wanting any help. Eventually he'd come up to pay for the part he'd selected that week. While paying for it, he'd always look you in the eye and say with all seriousness, "I'm building a ROBOT. I need some parts." The only details we could ever get out of him demonstrated he had no idea what he was doing. We'd smile while telling each other we "saw RobotMan" in an earlier shift, and it was always a burning question of what he'd buy next for his robot. Sure, he had no idea what he was doing, but who can fault a guy for having a goal and then trying his damnedest to get to that goal. He was just RobotMan to us, and we'd laugh while telling stories of his adventures in the store, but it was never done with malice.

After describing this, I'm all nostalgic for all those old characters.

The Admiral
Another one was "The Admiral". He was an old man, perhaps around 70-80 years of age. He had some kind of metal on the front of his shoes that would make a loud CLACK noise as he walked. Except he didn't walk. The Admiral marched everywhere he went. You could hear him coming before you could see him, with a "clack clack clack clack" getting louder as he got nearer. He was clearly demented, and carried a handheld radio frequency scanner with him. He constantly listened to police bands and would talk into it, responding to them. We knew the model he used, and it was a receive-only unit. Sometimes he'd say something loudly and come to attention and salute the air. Everybody had nothing but respect for him, and always took care of him kindly; he was probably the most well-treated customer we had. (He came to us to buy batteries for his scanner)

Crazy Ed
We had a manager named Ed. He is one of the best managers I ever had because of his honest positive motivation supporting his employees. Other than one character weakness that I could not condone (but was not my place to judge), he was a great guy as far as I'm concerned. He was also a little crazy. If you were reasonable to him, he'd be reasonable to you. More often he'd be more than reasonable and downright generous. And if you tried to fuck him over in some way, he would stomp you down. Ed was also built like a linebacker, with black eyes, one of them wandering. He was around 30 years old, and his size was physically imposing.

One Boxing Day, when there was a (predictably) busy store filled with people returning crap they had received for Christmas, I saw Customer Service Nirvanna. One guy came in to return a plant monitoring device. I checked his receipt and it said December 24. Anything on that short a timescale (2 days) was automatically returned, no questions asked, unless it was broken. This one was broken. He claimed it was already broken when he opened the box. It wasn't an unreasonable excuse and it was only two days, over Christmas and we'd been given orders to carte-blanche accept all returns from within the last two weeks of purchase. Just as I was about to process his refund, I realized that the year on the receipt was the wrong one - it was two days and one year since it had been purchased. We had a posted return policy of 14 days on anything, and the warranty on the part was 90 days. When I paused and pointed this out, he suddenly got a guilty look and stammered out "uh...well...yeah... I bought it last year but ...I just opened it and it was broken!" When he figured out that last part about just opening it, he looked happy again, like he had just figured how to wriggle out of an implicit lie. I told him I'd have to ask my manager about it, and I'd be right back.

Ed's open-door office was fully visible to a customer at the cashier's desk. I took it to Ed, explained the details of how this customer had most likely just tried to rip us off. Ed stared down the guy to make eye contact, threw the monitor on the ground, then stomped the living shit out of it for what seemed like a gleeful eternity while the guy looked on with pie plate deer-in-headlight eyes. Did I mention that Ed was built like a linebacker? Ed calmly gathered the tiny pieces together and gave them to me while he explained what I should do next:

I took the pieces back to the customer, put them on the desk in front of him, and told him "I'm sorry, we tried to fix it, but we just couldn't seem to get it to work." I paused for a few seconds, as Ed had said, "to let him think about what he just did", then smiled brightly and told him we'd be happy to replace his defective plant monitor at no charge. I gave him a brand new one in a store bag and apologized again for not being able to fix the old one. Needless to say, the new ex-customer looked scared, and he never came back to bother us again.

Ed was awesome. And crazy. I miss those days.

Burton MacKenZie www.burtonmackenzie.com

Dogs can sniff out CANCER

noreply@blogger.com (burton mackenzie) — Sat, 09 Aug 2008 07:16:00 +0000

Dogs can be trained to smell some types of CANCER! So far they have been proven to detect lung cancer, breast cancer, and skin cancer melanomas.

With this incredibly cost effective early warning system, getting smelled by the cancer dogs should be a repetitious ritual. Like going to see a dentist every six months. This detection method alone could save untold thousands of lives and billions of dollars every year!

This news is a few years old now, but it's the first I've heard of it. Why isn't this *everywhere* yet?

Burton MacKenZie www.burtonmackenzie.com

Two new electricity discoveries

noreply@blogger.com (burton mackenzie) — Fri, 01 Aug 2008 08:39:00 +0000

There are two new places in the universe we've found electricity at work!

First, for the first time in history, electric fields have been detected inside a human cell. Not only that, the electric fields detected are comparable in strength to lightning bolts! (remember: electric fields are in volts/metre, not volts. So, even a small voltage at tiny distances makes for a huge strength of electric field.) I can't wait for finer grained measurements. This probes a whole new level of how our bodies work!

Second, for the first time in history, electrical activity has been detected in the atmosphere of Titan. Titan, the largest moon of Saturn, is larger than Earth's moon and has an atmosphere of mostly Nitrogen, like Earth, and lots of hydrocarbons. The Huygens probe landed on it in 2005. It was hypothesized that if there were electrical activity (like lightning) in Titan's atmosphere, it would be detectable in information gathered by the Huygens mutual impedance sensor. First the analysis was tested with an analytical function, next with data generated from the computational mesh simulation of Titan's atmosphere, and finally with the actual data. The actual Huygens data shows Schumann resonances that are the expected fingerprint of Titan, matching the simulation results. If there's lightning in an atmosphere with hydrocarbons, you get the building blocks of life. Has any life been built there? I can't wait to find out.

Way to go, Science. Two thumbs up for beating back the darkness.

Burton MacKenZie www.burtonmackenzie.com

[1] Morente, J. A., Portí, J.A., Salinas, A., Navarro, E.A., “Evidence of electrical activity on Titan drawn from the Schumann resonances sent by Huygens probe”, Icarus, Volume 195, Issue 2, p802-811, 2008